Find the perimeter of the shape shown in
the diagram

The solution to the recursive relationship T(n) = 3T(n-1) + 1 with T(2) = 0 is T(n) = 3^(n-3) + 3^(n-4) + ... + 9 + 3 + 1.

To solve the recursive relationship T(n) = 3T(n-1) + 1, we can expand the recursion until we reach the base case.

T(n) = 3T(n-1) + 1

= 3(3T(n-2) + 1) + 1

= 3^2 T(n-2) + 3 + 1

= 3^2 (3T(n-3) + 1) + 3 + 1

= 3^3 T(n-3) + 3^2 + 3 + 1

= 3^i T(n-i) + 3^(i-1) + 3^(i-2) + ... + 3^2 + 3 + 1

We can continue this process until we reach T(2), which is the base case given as T(2) = 0.

Since we are looking to find T(n), we set n-i = 2 and solve for i:

n - i = 2

i = n - 2

Substituting this value back into the expanded recursion, we have:

T(n) = 3^(n-2) T(2) + 3^(n-2-1) + 3^(n-2-2) + ... + 3^2 + 3 + 1

Simplifying further, we get:

T(n) = 3^(n-2) * 0 + 3^(n-3) + 3^(n-4) + ... + 9 + 3 + 1

= 3^(n-3) + 3^(n-4) + ... + 9 + 3 + 1

Therefore, the solution to the recursive relationship T(n) = 3T(n-1) + 1, with the base case T(2) = 0, is T(n) = 3^(n-3) + 3^(n-4) + ... + 9 + 3 + 1.

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Answer:

35 interviews

Step-by-step explanation:

1. Find the rate

21/3 = 7 people an hour

2. Find how much she can do in 2 hours

7 x 2 = 14 interviews

3. Add the 2 numbers

21 + 14 = 35 interviews

Answer:

3rd option is correct

.......................

Now let's see slope:-

\(\\ \rm\Rrightarrow m=\dfrac{1+5}{-2}=\dfrac{6}{-2}=-3\)

Option C is correct

a. The probability of drawing a red ball from Box 1 is 30%.

b. If a red ball is drawn from Box 1, the probability of drawing another red ball from Box 2 on the second round is 60%.

c. If the first draw from Box 1 was black, the conditional probability of drawing a red ball from Box 3 on the second draw is 80%.

d. The probability of drawing two red balls at both draws, without any prior information, is 46%.

e. The probability of drawing a red ball at the first draw and a black ball at the second draw, without any prior information, is 21%.

a. The probability of drawing a red ball from Box 1 can be calculated by dividing the number of red balls in Box 1 by the total number of balls in Box 1. Therefore, the probability is 3/(3+7) = 3/10 = 0.3 or 30%.

b. Since a red ball was drawn from Box 1, we only consider the balls in Box 2. The probability of drawing a red ball from Box 2 is 6/(6+4) = 6/10 = 0.6 or 60%. Therefore, the probability of drawing another red ball when the first ball drawn from Box 1 is red is 60%.

c. If the first draw from Box 1 was black, we only consider the balls in Box 3. The probability of drawing a red ball from Box 3 is 8/(8+2) = 8/10 = 0.8 or 80%. Therefore, the conditional probability of drawing a red ball from Box 3 when the first ball drawn from Box 1 was black is 80%.

d. Before any draws, the probability of drawing two red balls at both draws can be calculated by multiplying the probabilities of drawing a red ball from Box 1 and a red ball from Box 2. Therefore, the probability is 0.3 * 0.6 = 0.18 or 18%. However, since there are two possible scenarios (drawing red balls from Box 1 and Box 2, or drawing red balls from Box 2 and Box 1), we double the probability to obtain 36%. Adding the individual probabilities of each scenario gives a total probability of 36% + 10% = 46%.

e. Before any draws, the probability of drawing a red ball at the first draw and a black ball at the second draw can be calculated by multiplying the probability of drawing a red ball from Box 1 and the probability of drawing a black ball from Box 2 or Box 3. The probability of drawing a red ball from Box 1 is 0.3, and the probability of drawing a black ball from Box 2 or Box 3 is (7/10) + (2/10) = 0.9. Therefore, the probability is 0.3 * 0.9 = 0.27 or 27%. However, since there are two possible scenarios (drawing a red ball from Box 1 and a black ball from Box 2 or drawing a red ball from Box 1 and a black ball from Box 3), we double the probability to obtain 54%. Adding the individual probabilities of each scenario gives a total probability of 54% + 10% = 64%.

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Answer:

tysm bestie

Step-by-step explanation:

Answer:

Step-by-step explanation:

this is confusing b/c they are asking about two trains traveling at differnt speeds, but.. if you put the speeds together and make one train... imaginary.. ofc... traveling at the speed of both trains combined... when will it be 50 miles from the station?

maybe you can solve that?   I'll solve it below.. but.. if you can.. try it now, on your own

below is my answer... don't look until you have solved yours :P

80+70= 150kph

when will this have traveled 50Km?

you may be able to see that it will take 1/3 of an hour to travel 50 km

so 60 minutes times 1/3 = 20 minutes  :)

Answer:

2x-2= -21

Step-by-step explanation:

Answer:

-9.5

Step-by-step explanation:

We can create an equation to represent this, where \(n\) is the missing value.

\(2n - 2 = -21\)

Now we can solve for \(n\) by isolating it on one side of the equation.

Add 2 to both sides:

\(2n - 2 + 2 = -21+2\\\\2n = -19\)

Divide both sides by 2:

\(2n\div2 = -19\div2\\\\n = -9.5\)

Hope this helped!

The solution to the equation 3x - 8u = v, given u = ⟨4, -1⟩ and v = ⟨-1, -3⟩, is x = ⟨31/3, -11/3⟩.

To solve the equation 3x - 8u = v for the unknown vector x = ⟨a, b⟩, we can use the properties of vectors.

Given u = ⟨4, -1⟩, v = ⟨-1, -3⟩, and x = ⟨a, b⟩, the equation can be rewritten as:

3x - 8u = v

Substituting the given values:

3⟨a, b⟩ - 8⟨4, -1⟩ = ⟨-1, -3⟩

Simplifying each component:

⟨3a, 3b⟩ - ⟨32, -8⟩ = ⟨-1, -3⟩

Combining like terms:

⟨3a - 32, 3b + 8⟩ = ⟨-1, -3⟩

Setting the corresponding components equal to each other:

3a - 32 = -1

3b + 8 = -3

Solving the first equation for a:

3a = -1 + 32

3a = 31

a = 31/3

Solving the second equation for b:

3b = -3 - 8

3b = -11

b = -11/3

Therefore, the solution to the equation 3x - 8u = v, given u = ⟨4, -1⟩ and v = ⟨-1, -3⟩, is x = ⟨31/3, -11/3⟩.

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If the margin of error is 4.6, the interval estimate would be the point estimate plus or minus 4.6.

In statistical estimation, the margin of error represents the maximum amount by which the point estimate may deviate from the true population parameter. It provides a measure of the precision or uncertainty associated with the estimate. When constructing a confidence interval, the margin of error is used to determine the range within which the true parameter is likely to fall.

To obtain the interval estimate, we add and subtract the margin of error from the point estimate. Let's denote the point estimate as x bar. Therefore, the interval estimate can be expressed as X bar ± 4.6, where ± denotes the range above and below the point estimate.

In summary, if the margin of error in an interval estimate of μ is 4.6, the interval estimate is given by the point estimate plus or minus 4.6. This range captures the likely range of values for the true population parameter μ.

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Answer:

(1/32)^(3/5) = 1/2^15.

(9)^(-3/2) = 1/27.

Step-by-step explanation:

To simplify the expressions:

(1/32)^(3/5):

To simplify this expression, we can raise the numerator and the denominator separately to the power of 3/5.

(1/32)^(3/5) = (1^(3/5))/(32^(3/5))

The numerator simplifies to 1^3 = 1, and the denominator simplifies to (2^5)^3 = 2^(5*3) = 2^15.

Therefore, the expression simplifies to:

(1/32)^(3/5) = 1/2^15.

(9)^(-3/2):

To simplify this expression, we can take the reciprocal of 9^3/2, which is equivalent to the square root of 9 cubed.

9^(3/2) = sqrt(9^3) = sqrt(999) = sqrt(729) = 27.

Taking the reciprocal gives:

(9)^(-3/2) = 1/27.

Therefore, the simplified expression is 1/27.

Answer: 42

Step-by-step explanation:

6 12 18 24 30 36 42

7 14 21 28 35 42

Answer:

The 42nd Voter

is the correct awnser!

We have a Ferris wheel with diameter D=73 ft.

Each revolution of the wheel a person will travel a distance equivalent to the circumference of the wheel. We can calculate the circumference of the wheel as:

If each ride the wheel makes 19 revolutions, we can calculate the distance by multiplying the distance travelled in each revolution by the number of revolutions per ride:

Answer: 4355.18 feet per ride.

Answer:

Subtract 1 from both sides.

Answer:

subtract 1 from both sides. because taking out the 1 from 1 and 1 from 17 will equal 16. which leaves t/4=16

We can say that after answering the offered question Hence, p > 8 is the equation inequality expressing the range of feasible values for p.

An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.

Let's use the letter "p" to indicate how many pounds Carmen will spend.

Candy is $7 for every pound.

Carmen's sweets expenditure is expressed as follows:

Cost per pound times the weight of the candy purchased is 7p.

Carmen will undoubtedly spend more than $56 on sweets, therefore we may say:

More than $56 was spent on candy

Using the following equation in place of the amount spent on candy:

7p > $56

When we multiply both sides by 7, we get:

p > 8

So, any figure more than 8 is a possibility for the amount of pounds Carmen will purchase. We can express this as follows:

p > 8

Hence, p > 8 is the inequality expressing the range of feasible values for p.

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Answer:

we can check the position of √7 is btw p and q

because square of 2 is 4 while square of 6 is 36

and 7 lies btw 4 and 36 therefore √7 lies btw p and Q

Answer:

OPTION C BETWEEN P AND Q

As 7 is equals to 2.78approx.

Step-by-step explanation:

..

The cost per passenger for quiescent is 222 dollars.

We have the given equation is:

The cost C (in dollars) per passenger is given by:

\(C(x) =100+\frac{x}{10}+\frac{36,000}{x}\)

where x is the ground speed.

Also have,

A Boeing 747 crosses the Atlantic Ocean (3000miles) with an airspeed of 500 miles per hour.

Now, According to the question:

and, according to the condition:

The equation is:

\(C(x) =100+\frac{x}{10}+\frac{36,000}{x}\)

\(C(500) =100+\frac{500}{10}+\frac{36,000}{500}\)

C(500) = 222 dollars

The speed of wind is 0 and ground speed is equal to airspeed.

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Answer:

Step-by-step explanation:

nose maffddnojgjfkufieo3owoeoiff

The shark travels a total vertical distance of 90 ft .The shark starts at a depth of 75 ft and jumps out of the water to a height of 15 ft. To calculate the total distance traveled by the shark.

we need to consider both the vertical distance it moves upwards and the initial depth it starts from.

The vertical distance traveled by the shark is the difference between the final height and the initial depth:

Vertical distance = 15 ft - (-75 ft) = 15 ft + 75 ft = 90 ft

Therefore, the shark travels a total vertical distance of 90 ft.

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Answer:

b) 2/6

Step-by-step explanation:

0, 1/6, 2/6, 3/6, 4/6, 5/6, 1

Hope this helps!

The distribution does not represent a probability distribution. The correct option is b.

A probability distribution should satisfy two main conditions: (1) the sum of the probabilities for all possible outcomes should be equal to 1, and (2) the probabilities for each outcome should be between 0 and 1 (inclusive).

In this distribution, the probabilities for the outcomes are 0.3, 0.4, 0.3, and 0.1 for the values of X as 3, 6, 9, and 0, respectively. However, the sum of these probabilities is 1.1, which violates the first condition of a probability distribution.

Therefore, this distribution does not meet the requirements of a probability distribution and is not a valid probability distribution. The correct answer is option b.

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\(7\frac{1}{2}\implies 7.5\hspace{5em}1\frac{1}{4}\implies 1.25 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{Monday through Friday} }{\stackrel{ days }{(5)}\stackrel{ rate }{(10.80)}\stackrel{ hours }{(7.5)}}~~ + ~~\stackrel{ Saturday }{\stackrel{ days }{(1)}\stackrel{ rate }{(10.80)(1.25)}\stackrel{ hours }{(7.5)}} \\\\\\ 405~~ + ~~101.25\implies \text{\LARGE 506.25}\)

k = 0 to 399 By calculating this summation, we will obtain the probability that Paul goes broke. To find the probability that Paul goes broke when Peter has a 2/3 probability of winning each game, we can use the concept of probability, game, and bet in our explanation.

First, we need to determine the probability of Paul winning a game, which can be found by subtracting Peter's winning probability from 1:

Probability of Paul winning = 1 - Probability of Peter winning = 1 - 2/3 = 1/3

Now, let's denote the number of games required for one of them to go broke as 'n'. Since they each start with $400, the total number of games would be n = 400 + 400 = 800.

We will use the binomial probability formula to calculate the probability of Paul going broke after 'n' games:

P(Paul goes broke) = (n! / (k!(n-k)!)) * (p^k) * (q^(n-k))

Here, n is the total number of games (800), k is the number of games Paul wins, p is the probability of Paul winning (1/3), and q is the probability of Peter winning (2/3).

To find the probability of Paul going broke, we need to calculate the probability of Paul winning fewer than 400 games out of 800:

P(Paul goes broke) = Σ [P(Paul wins 'k' games)] for k = 0 to 399

By calculating this summation, we will obtain the probability that Paul goes broke.

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a) Causal, memoryless, linear, time-invariant.

b) Causal, memoryless, linear, time-invariant.

c) Causal, memoryless, nonlinear, time-invariant.

d) Causal, has memory, nonlinear, time-invariant.

a) The system described by y[n] = x[n] + 2x[n+1] is causal because the output value at any time index n only depends on the current and past input values. It is memoryless since the output at a given time index n does not depend on any past or future inputs. The system is linear because the output is a linear combination of the input values. It is also time-invariant because the system's behavior remains unchanged over time.

b) The system y[n] = u[n]x[n] is causal since the output at any time index n only depends on the current and past input values. It is memoryless because the output at a given time index n does not depend on any past or future inputs. The system is linear because the output is a product of the input signal and a constant. It is also time-invariant because the system's behavior remains unchanged over time.

c) The system y[n] = |x[n]| is causal since the output at any time index n only depends on the current and past input values. It is memoryless because the output at a given time index n does not depend on any past or future inputs. The system is nonlinear because the absolute value operation is a nonlinear operation. It is time-invariant because the system's behavior remains unchanged over time.

d) The system y[n] = ∑(0.5)^n x[i] for i=0 to n is causal since the output at any time index n only depends on the current and past input values. It has memory because the output at a given time index n depends on all past input values up to the current time index. The system is nonlinear because the output is a sum of terms raised to a power, which is a nonlinear operation. It is time-invariant because the system's behavior remains unchanged over time.

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Answer:

56n - 35

Step-by-step explanation:

6n + 5(10n - 7) ← multiply each term in the parenthesis by 5

= 6n + 50n - 35 ← collect like terms

= 56n - 35

Answer:

2x + 3y = 33

Step-by-step explanation:

Hold on let me double check

To convert 1.05 x 10^-8 to standard form, we simply need to move the decimal point 8 places to the left, since the exponent is negative.

1.05 x 10^-8 = 0.0000000105

Therefore, 1.05 x 10^-8 in standard form is 0.0000000105.

Answer:

0.0000000105.

Step-by-step explanation:

Answer:

When a number is halfway between the two possible numbers, round up to the greater number. Since 186 is between 180 and 190, and 186 is closer to 190, you round up to 190. You can use a number line to help you round numbers.

Step-by-step explanation: